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A298122
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a(n) is the number of n nonintersecting arches above the x-axis that start and/or end with an arch length equal to one and have floor((n+2)/2) arches starting in odd numbered positions.
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0
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1, 1, 2, 5, 11, 34, 90, 300, 875, 3038, 9408, 33516, 108108, 392040, 1302444, 4785066, 16256955, 60324550, 208579800, 780088452, 2735682092, 10296854984, 36532677272, 138231751840, 495241833996, 1882201158264, 6799413051200, 25939319270000, 94374970110000
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OFFSET
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1,3
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LINKS
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FORMULA
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a(1) = a(2) = 1, a(3) = 2; for n > 3, a(n) = 2*(C(n-1, floor((n-1)/2))*C(n-2, floor((n-2)/2)) - (C(n-1, floor((n-2)/2))*C(n-2, floor((n-3)/2)))) - (C(n-3, floor((n-1)/2))*C(n-2, floor((n-1)/2))/(floor((n-1)/2)+1)).
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EXAMPLE
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Example: For n = 4 the a(4) = 5 solutions are as follows. (The numbers under the arches represent arches starting in an odd-numbered position on the x-axis.)
/\ /\
//\\ /\ /\ //\\ /\
///\\\/\, //\\ /\ /\, /\//\\/\, /\///\\\, /\/\//\\.
1 3 7 1 5 7 1 3 7 1 3 5 1 3 5
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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